Relating Reflex Gain Modulation in Posture Control to Underlying Neural Network Properties Using a Neuromusculoskeletal Model
Total Page:16
File Type:pdf, Size:1020Kb
J Comput Neurosci (2011) 30:555–565 DOI 10.1007/s10827-010-0278-8 Relating reflex gain modulation in posture control to underlying neural network properties using a neuromusculoskeletal model Jasper Schuurmans · Frans C. T. van der Helm · Alfred C. Schouten Received: 25 March 2010 / Revised: 1 September 2010 / Accepted: 14 September 2010 / Published online: 24 September 2010 © The Author(s) 2010. This article is published with open access at Springerlink.com Abstract During posture control, reflexive feedback the neural, sensory and synaptic parameters on the joint allows humans to efficiently compensate for unpre- dynamics. The results showed that the lumped reflex dictable mechanical disturbances. Although reflexes gains positively correlate to their most direct neural are involuntary, humans can adapt their reflexive set- substrates: the velocity gain with Ia afferent velocity tings to the characteristics of the disturbances. Reflex feedback, the positional gain with muscle stretch over modulation is commonly studied by determining reflex II afferents and the force feedback gain with Ib afferent gains: a set of parameters that quantify the contribu- feedback. However, position feedback and force feed- tions of Ia, Ib and II afferents to mechanical joint be- back gains show strong interactions with other neural havior. Many mechanisms, like presynaptic inhibition and sensory properties. These results give important and fusimotor drive, can account for reflex gain mod- insights in the effects of neural properties on joint ulations. The goal of this study was to investigate the dynamics and in the identifiability of reflex gains in effects of underlying neural and sensory mechanisms experiments. on mechanical joint behavior. A neuromusculoskeletal model was built, in which a pair of muscles actuated a Keywords Reflexes · Afferent feedback · Reflex limb, while being controlled by a model of 2,298 spiking gains · Sensitivity analysis · System identification neurons in six pairs of spinal populations. Identical to experiments, the endpoint of the limb was disturbed with force perturbations. System identification was 1 Introduction used to quantify the control behavior with reflex gains. A sensitivity analysis was then performed on the neu- During posture control, humans have two strategies romusculoskeletal model, determining the influence of to counteract unexpected disturbances and keep their equilibrium position. Co-contraction of the muscles increases joint viscoelasticity, while maintaining equi- Action Editor: Simon R. Schultz librium. Co-contraction provides instantaneous vis- The model presented in this article is available on our coelasticity at the expense of high metabolic energy department’s website: http://nmc.3me.tudelft.nl. consumption. Sensory feedback is energy efficient, al- J. Schuurmans (B) · F. C. T. van der Helm · A. C. Schouten though effectiveness is limited due to the inherent Department of Biomechanical Engineering, neural time delays. Delft University of Technology, Mekelweg 2, In the presence of fast unpredictable disturbances 2628 CD Delft, The Netherlands e-mail: [email protected] in the upper extremity, reflexes through afferent feed- back provided by muscle spindles and Golgi tendon F. C. T. van der Helm · A. C. Schouten organs are the major contributors to sensory feedback. Laboratory of Biomechanical Engineering, MIRA Institute Muscle spindles are located in the muscles and provide for Biomedical Technology and Technical Medicine, University of Twente, P.O. Box 217, feedback on stretch and stretch velocity. Golgi tendon 7500 AE Enschede, The Netherlands organs are located in the junction between muscle and 556 J Comput Neurosci (2011) 30:555–565 tendon, providing feedback on muscle force. Reflexes goal of this study was to investigate how neural and are involuntary responses to stimuli, and their strength sensory properties could map onto the (limited) set of is known to be modulated. Experiments have shown reflex gains as obtained from joint dynamics, using a that different task instructions (Doemges and Rack neuromusculoskeletal model. In other words: how do 1992a, b; Abbink et al. 2004), disturbance properties the underlying, physical neural and sensory properties (de Vlugt et al. 2002) and dynamic properties of the effectively link to the lumped reflex gains? We used environment (Van der Helm et al. 2002) all elicit adap- a neuromusculoskeletal model of a spinal neural net- tation of the reflexive contribution to joint dynamics. work controlling an antagonistic pair of muscles with Model simulations have indicated that these reflex set- afferent feedback (Stienen et al. 2007). In a sensitivity tings are close to optimal for suppressing the distur- analysis, sensory and neural properties in the model bances (Schouten et al. 2001). were systematically varied and reflex experiments were Additional to the many studies that quantify simulated to determine reflex gains. The results showed reflexive behavior by directly deriving metrics like in- that besides the expected mappings, there also exist tegrated EMG after the application of a mechanical intricate, counterintuitive relationships between neural or electrical stimulus (e.g. Dewald and Schmit 2003; and sensory properties and reflex gains that need to Schuurmans et al. 2009; Kurtzer et al. 2008; Nielsen be taken into account when interpreting experimental et al. 2005), other studies use a control engineering results. approach to parameterize joint dynamics. A combi- nation of system identification and modeling is then used to separate muscular and reflexive contributions 2 Methods (Kearney et al. 1997; Perreault et al. 2000;Vander Helm et al. 2002; Ludvig and Kearney 2007; Schouten 2.1 Approach et al. 2008a). The dynamic behavior of the joint is estimated by perturbing the joint with a random force Posture control experiments around the shoulder joint disturbance using a robotic manipulandum and record- (Van der Helm et al. 2002) were mimicked on a ing displacement and interaction force between the neuromusculoskeletal (NMS) model. In these types of subject and the manipulandum. The joint dynamics are experiments, a subject holds the handle of a linear expressed in terms of the mechanical admittance, de- manipulator and minimizes deviations while being per- scribing the amount of displacement per unit force. To turbed with a random force disturbance. This type of separate reflexive contributions from muscle viscoelas- posture control experiment was mimicked by perturb- ticity, lumped parameters (Schouten et al. 2008b)can ing a joint in a neuromusculoskeletal model with a be fitted to the mechanical admittance. The resulting continuous random force disturbance. The reflexive set of parameters quantify the joint inertia, the muscle contributions to the dynamic behavior of the joint viscoelasticity and the reflexive gains of the force, posi- were determined using system identification techniques tion and velocity feedback pathways. identical to experiments in vivo. The reflexive com- There are multiple mechanisms that affect the ponent was expressed in terms of reflex gains, which strength of the reflex pathway. Fusimotor drive (Crowe gave a quantitative measure for the amount of stretch, and Matthews 1964; Ribot-Ciscar et al. 2009) mod- stretch velocity and force related reflex action. In the ulates the muscle spindle’s sensitivity to stretch and sensitivity analysis the model parameters were system- stretch velocity, therewith altering the gain of the reflex atically varied and the effects on task performance, pathway. With presynaptic inhibition (Rudomin and joint admittance and the reflex gains were determined. Schmidt 1999; Rudomin 2009; Baudry et al. 2010), the efficacy of transmission between primary afferent fibers 2.2 Model description and the receiving neurons can be centrally modulated. The strengths of interneuronal connections in the spinal The NMS model is briefly described here; for full cord affect the net amount of activation of the mo- details see Stienen et al. (2007). Posture control of toneuron pool due to the sensory feedback. All these the shoulder was modeled as a one degree of free- mechanisms contribute to the joint dynamics as deter- dom joint (inertia m = 0.18 kg m2), actuated by an an- mined experimentally. tagonistic pair of muscles (moment arm rm = 30 mm). Despite the known neural mechanisms of reflex Since the experiment involved only small deviations modulation and the available identification techniques, around a constant level of co-contraction (≈40% of there are still many unknowns on how exactly neural maximal force), a linearized muscle model was used. mechanisms affect the measured joint dynamics. The The viscoelasticity due to muscle co-contraction was J Comput Neurosci (2011) 30:555–565 557 IA IA Legend set, such that the rotational viscoelasticity of the model 196 196 was equivalent to the translational viscoelasticity taken Neurons: XX Population of n from experimental data (Van der Helm et al. 2002): RC RC n neurons of type XX 196 196 the endpoint stiffness and viscosity of the arm were Synapses: respectively 800 N/m and 40 Ns/m. Stiffness and vis- MN Eff. Eff. MN Excitatory cosity represented cross-bridge viscoelasticity, which is 169 169 Excitatory, double strength dominant in an experiment with co-contraction and Excitatory, long time constant IN EX EX IN Tonic descending excitation relatively small displacements. The muscle activation 196 196 196 196 dynamics were of first order with